Question

A sum of money becomes 7 times itself in 2 years at a certain rate of simple interest. Find the rate of interest per annum.

• A. 100%
• B. 10%
• C. 200%
• D. 300%

Hint:

For these problems, you can use the direct formula: $R = \frac{(n-1) \times 100}{T}$. Here, $R = \frac{(7-1) \times 100}{2} = \frac{600}{2} = 300\%$.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Simple interest (SI) is calculated on the principal amount. When a sum "becomes $n$ times," it means the Amount ($A$) is $n \times P$, where $P$ is the Principal.

Step 2: Key Formula or Approach:
1. $SI = A - P$
2. $SI = \frac{P \times R \times T}{100}$

Step 3: Detailed Explanation:
Let Principal ($P$) = $x$. Then, Amount ($A$) = $7x$. Time ($T$) = 2 years. Simple Interest ($SI$) = $A - P = 7x - x = 6x$. Now, using the SI formula: \[ 6x = \frac{x \times R \times 2}{100} \] \[ 6 = \frac{2R}{100} \] \[ 3 = \frac{R}{100} \] \[ R = 300\% \]

Step 4: Final Answer:
The rate of interest per annum is 300%.